Board Paper of Class 12 2020 Physics - Solutions

All questions are compulsory.
This question paper is divided into 4 Sections, A, B, C and D as follows:
Section A
Question number 1 is of twelve marks. All parts of this question are compulsory.
Section B
Question numbers 2 to 12 carry 2 marks each with two questions having internal choice.
Section C
Question numbers 13 to 19 carry 3 marks each with two questions having internal choice.
Section D
Question numbers 20 to 22 are long-answer type questions and carry 5 marks each. Each question has an internal choice.
The intended marks for questions are given in brackets [ ].
All working, including rough work, should be done on the same sheet as and adjacent to the rest of the answer.
Answers to sub parts of the same question must be given in one place only. A list of useful physical constants is given at the end of this paper.
A simple scientific calculator without a programmable memory may be used for calculations.
Useful Constant and Relation:

931MeV

Question 1
(a) Choose the correct alternative (a), (b), (c) or (d) for each of the questions given below:
(i) A point charge ‘q’ is kept at each of the vertices of an equilateral triangle having each side ‘a’. Total electrostatic potential energy of the system is:
(a) $(\frac{1}{4 π ε_{0}}) \frac{3 q^{2}}{a^{2}}$
(b) $(\frac{1}{4 π ε_{0}}) \frac{3 q}{a}$
(c) $(\frac{1}{4 π ε_{0}}) \frac{3 q^{2}}{a^{}}$
(d) $(\frac{1}{4 π ε_{0}}) \frac{3 q}{a^{2}}$

(ii) Curie temperature is the temperature above which:
(a) a ferromagnetic substance behaves like a paramagnetic substance.
(b) a paramagnetic substance behaves like a diamagnetic substance.
(c) a ferromagnetic substance behaves like a diamagnetic substance.
(d) a paramagnetic substance behaves like a ferromagnetic substance.

(iii) In an astronomical telescope of refracting type:
(a) Objective should have small focal length.
(b) Objective should have large focal length.
(c) Eyepiece should have large focal length.
(d) Both objective and eyepiece should have large focal length.

(iv) In photoelectric effect experiment, the slope of the graph of the stopping potential versus frequency gives the value of:
(a) $\frac{h}{e}$
(b) h
(c) $\frac{e}{h}$
(d) $\frac{h c}{e}$

(v) In a nuclear reactor, cadmium rods are used as:
(a) Control rods
(b) Fuel rods
(c) Coolant
(d) Moderator

(b) Answer the following questions briefly and to the point:
(i) State Gauss’ theorem.
(ii) A metallic wire having a resistance of 20Ω is bent in order to form a complete circle. Calculate the resistance between any two diametrically opposite points on the circle.
(iii) How can a moving coil galvanometer be converted into a voltmeter?
(iv) Write Biot-Savart’s law in vector form.
(v) What is the phase difference between any two points lying on the same wavefront?
(vi) Name the physical principle on the basis of which optical fibres work.
(vii) What is Pair production? VIEW SOLUTION

Question 2
A uniform copper wire having a cross sectional area of 1mm² carries a current of 5A. Calculate the drift speed of free electrons in it.
(Free electron number density of copper = 2 × 10²⁸/m³)
OR

An electric bulb is rated as 250V, 750W. Calculate the:
(i) Electric current flowing through it, when it is operated on a 250V supply.
(ii) Resistance of its filament. VIEW SOLUTION

Question 3
Write an expression for force per unit length between two long current carrying wires, kept parallel to each other, in vacuum and hence define an ampere, the SI unit of current. VIEW SOLUTION

Question 4
(i) Define angle of dip.
(ii) State the relation between magnetic susceptibility $(χ)$ and relative permeability (µ_r) of a magnetic substance. VIEW SOLUTION

Question 5
(a) Figure 1 below shows a metallic rod MN of length l = 80 cm, kept in a uniform magnetic field of flux density B = 0·5 T, on two parallel metallic rails P and Q.
Calculate the emf that will be induced between its two ends, when it is moved towards right with a constant velocity v of 36 km/hr.

OR

(b) When current flowing through one coil changes from 0 Amp to 15 Amp in 0·2 s, an emf of 750V is induced in an adjacent coil.
Calculate the coefficient of mutual inductance of the two coils.
VIEW SOLUTION

Question 6
(i) State any one use of infrared radiations.
(ii) State any one source of ultraviolet radiations. VIEW SOLUTION

Question 7
Where will you keep an object in front of a:
(i) Convex lens in order to get a virtual and magnified image?
(ii) Concave mirror to get a real and diminished image? VIEW SOLUTION

Question 8
Draw a labelled graph of angle of deviation (𝛿) versus angle of incidence (i) for a prism. VIEW SOLUTION

Question 9
(i) State de Broglie hypothesis.
(ii) What conclusion can be drawn from Davisson and Germer’s experiment? VIEW SOLUTION

Question 10
Calculate binding energy of oxygen nucleus $({}_{8}^{16}O)$ from the data given below:
Mass of a proton = 1·007825u
Mass of a neutron = 1·008665u
Mass of $({}_{8}^{16}O)$ = 15·994915u VIEW SOLUTION

Question 11
For a radioactive substance, write the relation between:
(i) Half life (T) and disintegration constant (λ).
(ii) Mean life (τ) and disintegration constant (λ). VIEW SOLUTION

Question 12
With reference to communication systems, what is meant by:
(i) modulation?
(ii) demodulation? VIEW SOLUTION

Question 13
Show that intensity of electric field E at a point in broadside on position is given by:
$E = (\frac{1}{4 π \in_{0}}) \frac{p}{{(r^{2} + l^{2})}^{3 / 2}}$ , where the terms have their usual meaning. VIEW SOLUTION

Question 14
A parallel plate capacitor is charged by a battery, which is then disconnected. A dielectric slab having dielectric constant (relative permittivity) K, is now introduced between its two plates in order to occupy the space completely. State, in terms of K, its effect on the following:
(i) The capacitance of the capacitor.
(ii) The potential difference between its plates.
(iii) The energy stored in the capacitor. VIEW SOLUTION

Question 15
(a) E₁ and E₂ are two batteries having emfs of 3V and 4V and internal resistances of 2Ω and 1Ω respectively. They are connected as shown in Figure 2 below.
Using Kirchhoff’s Laws of electrical circuits, calculate the currents I₁ and I₂.

OR

(b) A potentiometer circuit is shown in Figure 3 below. AB is a uniform metallic wire having length of 2m and resistance of 8Ω.
The batteries E₁and E₂ have emfs of 4V and 1·5V and their internal resistances are 1Ω and 2Ω respectively.

(i) When the jockey J does not touch the wire AB, calculate:

(a) the current flowing through the potentiometer wire AB.
(b) the potential gradient across the wire AB.

(ii) Now the jockey J is made to touch the wire AB at a point C such that the galvanometer (G) shows no deflection. Calculate the length AC.
VIEW SOLUTION

Question 16
For two thin lenses kept in contact with each other, show that:
$\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$
where the terms have their usual meaning. VIEW SOLUTION

Question 17
(a) A compound microscope consists of two convex lenses having focal length of 1·5cm and 5cm.
When an object is kept at a distance of 1·6cm from the objective, the final image is virtual and lies at a distance of 25cm from the eyepiece.
Calculate magnifying power of the compound microscope in this set-up.

OR

(b) In Young’s double slit experiment, the screen is kept at a distance of 1·2m from the plane of the slits.
The two slits are separated by 5mm and illuminated with monochromatic light having wavelength 600nm.
Calculate:
(i) Fringe width i.e. fringe separation of the interference pattern.
(ii) Distance of 10^th bright fringe from the centre of the pattern.
VIEW SOLUTION

Question 18
Draw the energy level diagram of hydrogen atom and show the transitions responsible for:
(i) absorption lines of Lyman series.
(ii) emission lines of Balmer series. VIEW SOLUTION

Question 19
(i) State any one difference between energy band diagram of conductors and that of insulators.
(ii) Give a relation between 𝛼 and 𝛽 for a transistor.
(Derivation is not required.)
(iii) What is the advantage of an LED bulb over the filament electric bulb? VIEW SOLUTION

Question 20
(i) A 400Ω resistor, a 3H inductor and a 5μF capacitor are connected in series to a 220V, 50Hz ac source. Calculate the:
(1) Impedance of the circuit.
(2) Current flowing through the circuit.

(ii) Draw a labelled graph showing the variation of impedance (Z) of a series LCR circuit versus frequency (f) of the ac supply.
OR

(i) When an alternating emf e = 310 sin (100𝜋t)V is applied to a series LCR circuit, current flowing through it is i = 5 sin(100𝜋t + 𝜋/3)A.
(1) What is the phase difference between the current and the emf?
(2) Calculate the average power consumed by the circuit.

(ii) Obtain an expression for the resonant frequency (f_o) of a series LCR circuit. VIEW SOLUTION

Question 21
(i) Derive an expression for refraction at a single (convex) spherical surface, i.e. a relation between u, v, R, n₁ (rarer medium) and n₂(denser medium), where the terms have their usual meaning.
(ii) Name the phenomenon due to which the sun appears reddish at sunset.
OR

(i) Draw a labelled graph of intensity of diffracted light (I) versus angle (𝜃) in the Fraunhofer diffraction experiment for a single slit diffraction.
(ii) State the law of Malus.
(iii) How will you distinguish experimentally between ordinary light and plane polarized light? VIEW SOLUTION

Question 22
(i) In a semiconductor diode, what is meant by potential barrier?
(ii) Draw a labelled circuit diagram of a Zener diode as a voltage regulator.
(iii) Show with the help of a diagram, how you will obtain an AND gate using only NAND gates. (Truth table is not required.)
OR

(i) Draw a labelled circuit diagram of a transistor acting as a common emitter amplifier. What is meant by phase reversal?

(ii) Draw the symbol of a NAND gate and write its truth table. VIEW SOLUTION